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Ideas for 'works', 'The Philosophy of Mathematics' and 'Introduction to the Philosophy of Mathematics'

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7 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

9195	Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]

17924

Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]

5. Theory of Logic / E. Structures of Logic / 1. Logical Form

4730	For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]

5. Theory of Logic / G. Quantification / 5. Second-Order Quantification

9186	First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

9187	Logical truths and inference are characterized either syntactically or semantically [Dummett]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17929

Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

17930

Axioms are 'categorical' if all of their models are isomorphic [Colyvan]